In fact "mal" as an adjective is a short form for "malo" which is the adjective.
Example: Olor malo ->Mal olor (Bad smell)
The adjective of good is "Bueno" or the short form "Buen"
If you say "estoy mal" then "mal" is also and adverb.
So "bien" and "mal" are both adverbs in the sentences you wrote.
Notice that both words are modifying the verb "Sentir" or "estar" so they are adverbs in both cases.
I hope it helps.